/*
 * NFA utilities.
 * This file is #included by regcomp.c.
 *
 * Copyright (c) 1998, 1999 Henry Spencer.	All rights reserved.
 *
 * Development of this software was funded, in part, by Cray Research Inc.,
 * UUNET Communications Services Inc., Sun Microsystems Inc., and Scriptics
 * Corporation, none of whom are responsible for the results.  The author
 * thanks all of them.
 *
 * Redistribution and use in source and binary forms -- with or without
 * modification -- are permitted for any purpose, provided that
 * redistributions in source form retain this entire copyright notice and
 * indicate the origin and nature of any modifications.
 *
 * I'd appreciate being given credit for this package in the documentation
 * of software which uses it, but that is not a requirement.
 *
 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
 * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
 * AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL
 * HENRY SPENCER BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
 * OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
 * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
 * OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
 * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * $PostgreSQL: pgsql/src/backend/regex/regc_nfa.c,v 1.7 2009/06/11 14:49:01
 * momjian Exp $
 *
 *
 * One or two things that technically ought to be in here
 * are actually in color.c, thanks to some incestuous relationships in
 * the color chains.
 */

#define NISERR() VISERR(nfa->v)
#define NERR(e) VERR(nfa->v, (e))

/*
 * newnfa - set up an NFA
 */
static struct nfa * /* the NFA, or NULL */
newnfa(struct vars *v, struct colormap *cm,
       struct nfa *parent) /* NULL if primary NFA */
{
  struct nfa *nfa;

  nfa = (struct nfa *)MALLOC(sizeof(struct nfa));
  if (nfa == NULL) return NULL;

  nfa->states = NULL;
  nfa->slast = NULL;
  nfa->free = NULL;
  nfa->nstates = 0;
  nfa->cm = cm;
  nfa->v = v;
  nfa->size = 0;
  nfa->bos[0] = nfa->bos[1] = COLORLESS;
  nfa->eos[0] = nfa->eos[1] = COLORLESS;
  nfa->parent = parent;            /* Precedes newfstate so parent is valid. */
  nfa->post = newfstate(nfa, '@'); /* number 0 */
  nfa->pre = newfstate(nfa, '>');  /* number 1 */

  nfa->init = newstate(nfa); /* may become invalid later */
  nfa->final = newstate(nfa);
  if (ISERR()) {
    freenfa(nfa);
    return NULL;
  }
  rainbow(nfa, nfa->cm, PLAIN, COLORLESS, nfa->pre, nfa->init);
  newarc(nfa, '^', 1, nfa->pre, nfa->init);
  newarc(nfa, '^', 0, nfa->pre, nfa->init);
  rainbow(nfa, nfa->cm, PLAIN, COLORLESS, nfa->final, nfa->post);
  newarc(nfa, '$', 1, nfa->final, nfa->post);
  newarc(nfa, '$', 0, nfa->final, nfa->post);

  if (ISERR()) {
    freenfa(nfa);
    return NULL;
  }
  return nfa;
}

/*
 * TooManyStates - checks if the max states exceeds the compile-time value
 */
static int TooManyStates(struct nfa *nfa) {
  struct nfa *parent = nfa->parent;
  size_t sz = nfa->size;

  while (parent != NULL) {
    sz = parent->size;
    parent = parent->parent;
  }
  if (sz > REG_MAX_STATES) return 1;
  return 0;
}

/*
 * IncrementSize - increases the tracked size of the NFA and its parents.
 */
static void IncrementSize(struct nfa *nfa) {
  struct nfa *parent = nfa->parent;

  nfa->size++;
  while (parent != NULL) {
    parent->size++;
    parent = parent->parent;
  }
}

/*
 * DecrementSize - decreases the tracked size of the NFA and its parents.
 */
static void DecrementSize(struct nfa *nfa) {
  struct nfa *parent = nfa->parent;

  nfa->size--;
  while (parent != NULL) {
    parent->size--;
    parent = parent->parent;
  }
}

/*
 * freenfa - free an entire NFA
 */
static void freenfa(struct nfa *nfa) {
  struct state *s;

  while ((s = nfa->states) != NULL) {
    s->nins = s->nouts = 0; /* don't worry about arcs */
    freestate(nfa, s);
  }
  while ((s = nfa->free) != NULL) {
    nfa->free = s->next;
    destroystate(nfa, s);
  }

  nfa->slast = NULL;
  nfa->nstates = -1;
  nfa->pre = NULL;
  nfa->post = NULL;
  FREE(nfa);
}

/*
 * newstate - allocate an NFA state, with zero flag value
 */
static struct state * /* NULL on error */
newstate(struct nfa *nfa) {
  struct state *s;

  if (TooManyStates(nfa)) {
    NERR(REG_ETOOBIG);
    return NULL;
  }
  if (nfa->free != NULL) {
    s = nfa->free;
    nfa->free = s->next;
  } else {
    s = (struct state *)MALLOC(sizeof(struct state));
    if (s == NULL) {
      NERR(REG_ESPACE);
      return NULL;
    }
    s->oas.next = NULL;
    s->free = NULL;
    s->noas = 0;
  }

  assert(nfa->nstates >= 0);
  s->no = nfa->nstates++;
  s->flag = 0;
  if (nfa->states == NULL) nfa->states = s;
  s->nins = 0;
  s->ins = NULL;
  s->nouts = 0;
  s->outs = NULL;
  s->tmp = NULL;
  s->next = NULL;
  if (nfa->slast != NULL) {
    assert(nfa->slast->next == NULL);
    nfa->slast->next = s;
  }
  s->prev = nfa->slast;
  nfa->slast = s;
  /* track the current size and the parent size */
  IncrementSize(nfa);
  return s;
}

/*
 * newfstate - allocate an NFA state with a specified flag value
 */
static struct state * /* NULL on error */
newfstate(struct nfa *nfa, int flag) {
  struct state *s;

  s = newstate(nfa);
  if (s != NULL) s->flag = (char)flag;
  return s;
}

/*
 * dropstate - delete a state's inarcs and outarcs and free it
 */
static void dropstate(struct nfa *nfa, struct state *s) {
  struct arc *a;

  while ((a = s->ins) != NULL) freearc(nfa, a);
  while ((a = s->outs) != NULL) freearc(nfa, a);
  freestate(nfa, s);
}

/*
 * freestate - free a state, which has no in-arcs or out-arcs
 */
static void freestate(struct nfa *nfa, struct state *s) {
  assert(s != NULL);
  assert(s->nins == 0 && s->nouts == 0);

  s->no = FREESTATE;
  s->flag = 0;
  if (s->next != NULL)
    s->next->prev = s->prev;
  else {
    assert(s == nfa->slast);
    nfa->slast = s->prev;
  }
  if (s->prev != NULL)
    s->prev->next = s->next;
  else {
    assert(s == nfa->states);
    nfa->states = s->next;
  }
  s->prev = NULL;
  s->next = nfa->free; /* don't delete it, put it on the free list */
  nfa->free = s;
  DecrementSize(nfa);
}

/*
 * destroystate - really get rid of an already-freed state
 */
static void destroystate(struct nfa *nfa, struct state *s) {
  struct arcbatch *ab;
  struct arcbatch *abnext;

  assert(s->no == FREESTATE);
  for (ab = s->oas.next; ab != NULL; ab = abnext) {
    abnext = ab->next;
    FREE(ab);
  }
  s->ins = NULL;
  s->outs = NULL;
  s->next = NULL;
  FREE(s);
}

/*
 * newarc - set up a new arc within an NFA
 */
static void newarc(struct nfa *nfa, int t, pcolor co, struct state *from,
                   struct state *to) {
  struct arc *a;

  assert(from != NULL && to != NULL);

  /* check for duplicates */
  for (a = from->outs; a != NULL; a = a->outchain)
    if (a->to == to && a->co == co && a->type == t) return;

  a = allocarc(nfa, from);
  if (NISERR()) return;
  assert(a != NULL);

  a->type = t;
  a->co = (color)co;
  a->to = to;
  a->from = from;

  /*
   * Put the new arc on the beginning, not the end, of the chains. Not only
   * is this easier, it has the very useful side effect that deleting the
   * most-recently-added arc is the cheapest case rather than the most
   * expensive one.
   */
  a->inchain = to->ins;
  to->ins = a;
  a->outchain = from->outs;
  from->outs = a;

  from->nouts++;
  to->nins++;

  if (COLORED(a) && nfa->parent == NULL) colorchain(nfa->cm, a);
}

/*
 * allocarc - allocate a new out-arc within a state
 */
static struct arc * /* NULL for failure */
allocarc(struct nfa *nfa, struct state *s) {
  struct arc *a;

  /* shortcut */
  if (s->free == NULL && s->noas < ABSIZE) {
    a = &s->oas.a[s->noas];
    s->noas++;
    return a;
  }

  /* if none at hand, get more */
  if (s->free == NULL) {
    struct arcbatch *newAb;
    int i;

    newAb = (struct arcbatch *)MALLOC(sizeof(struct arcbatch));
    if (newAb == NULL) {
      NERR(REG_ESPACE);
      return NULL;
    }
    newAb->next = s->oas.next;
    s->oas.next = newAb;

    for (i = 0; i < ABSIZE; i++) {
      newAb->a[i].type = 0;
      newAb->a[i].freechain = &newAb->a[i + 1];
    }
    newAb->a[ABSIZE - 1].freechain = NULL;
    s->free = &newAb->a[0];
  }
  assert(s->free != NULL);

  a = s->free;
  s->free = a->freechain;
  return a;
}

/*
 * freearc - free an arc
 */
static void freearc(struct nfa *nfa, struct arc *victim) {
  struct state *from = victim->from;
  struct state *to = victim->to;
  struct arc *a;

  assert(victim->type != 0);

  /* take it off color chain if necessary */
  if (COLORED(victim) && nfa->parent == NULL) uncolorchain(nfa->cm, victim);

  /* take it off source's out-chain */
  assert(from != NULL);
  assert(from->outs != NULL);
  a = from->outs;
  if (a == victim) /* simple case:  first in chain */
    from->outs = victim->outchain;
  else {
    for (; a != NULL && a->outchain != victim; a = a->outchain) continue;
    assert(a != NULL);
    a->outchain = victim->outchain;
  }
  from->nouts--;

  /* take it off target's in-chain */
  assert(to != NULL);
  assert(to->ins != NULL);
  a = to->ins;
  if (a == victim) /* simple case:  first in chain */
    to->ins = victim->inchain;
  else {
    for (; a != NULL && a->inchain != victim; a = a->inchain) continue;
    assert(a != NULL);
    a->inchain = victim->inchain;
  }
  to->nins--;

  /* clean up and place on free list */
  victim->type = 0;
  victim->from = NULL; /* precautions... */
  victim->to = NULL;
  victim->inchain = NULL;
  victim->outchain = NULL;
  victim->freechain = from->free;
  from->free = victim;
}

/*
 * hasnonemptyout - Does state have a non-EMPTY out arc?
 */
static int hasnonemptyout(struct state *s) {
  struct arc *a;

  for (a = s->outs; a != NULL; a = a->outchain) {
    if (a->type != EMPTY) return 1;
  }
  return 0;
}

/*
 * nonemptyouts - count non-EMPTY out arcs of a state
 */
static int nonemptyouts(struct state *s) {
  int n = 0;
  struct arc *a;

  for (a = s->outs; a != NULL; a = a->outchain) {
    if (a->type != EMPTY) n++;
  }
  return n;
}

/*
 * nonemptyins - count non-EMPTY in arcs of a state
 */
static int nonemptyins(struct state *s) {
  int n = 0;
  struct arc *a;

  for (a = s->ins; a != NULL; a = a->inchain) {
    if (a->type != EMPTY) n++;
  }
  return n;
}

/*
 * findarc - find arc, if any, from given source with given type and color
 * If there is more than one such arc, the result is random.
 */
static struct arc *findarc(struct state *s, int type, pcolor co) {
  struct arc *a;

  for (a = s->outs; a != NULL; a = a->outchain)
    if (a->type == type && a->co == co) return a;
  return NULL;
}

/*
 * cparc - allocate a new arc within an NFA, copying details from old one
 */
static void cparc(struct nfa *nfa, struct arc *oa, struct state *from,
                  struct state *to) {
  newarc(nfa, oa->type, oa->co, from, to);
}

/*
 * moveins - move all in arcs of a state to another state
 *
 * You might think this could be done better by just updating the
 * existing arcs, and you would be right if it weren't for the desire
 * for duplicate suppression, which makes it easier to just make new
 * ones to exploit the suppression built into newarc.
 */
static void moveins(struct nfa *nfa, struct state *oldState,
                    struct state *newState) {
  struct arc *a;

  assert(oldState != newState);

  while ((a = oldState->ins) != NULL) {
    cparc(nfa, a, a->from, newState);
    freearc(nfa, a);
  }
  assert(oldState->nins == 0);
  assert(oldState->ins == NULL);
}

/*
 * copyins - copy in arcs of a state to another state
 *
 * Either all arcs, or only non-empty ones as determined by all value.
 */
static void copyins(struct nfa *nfa, struct state *oldState,
                    struct state *newState, int all) {
  struct arc *a;

  assert(oldState != newState);

  for (a = oldState->ins; a != NULL; a = a->inchain) {
    if (all || a->type != EMPTY) cparc(nfa, a, a->from, newState);
  }
}

/*
 * moveouts - move all out arcs of a state to another state
 */
static void moveouts(struct nfa *nfa, struct state *oldState,
                     struct state *newState) {
  struct arc *a;

  assert(oldState != newState);

  while ((a = oldState->outs) != NULL) {
    cparc(nfa, a, newState, a->to);
    freearc(nfa, a);
  }
}

/*
 * copyouts - copy out arcs of a state to another state
 *
 * Either all arcs, or only non-empty ones as determined by all value.
 */
static void copyouts(struct nfa *nfa, struct state *oldState,
                     struct state *newState, int all) {
  struct arc *a;

  assert(oldState != newState);

  for (a = oldState->outs; a != NULL; a = a->outchain) {
    if (all || a->type != EMPTY) cparc(nfa, a, newState, a->to);
  }
}

/*
 * cloneouts - copy out arcs of a state to another state pair, modifying type
 */
static void cloneouts(struct nfa *nfa, struct state *old, struct state *from,
                      struct state *to, int type) {
  struct arc *a;

  assert(old != from);

  for (a = old->outs; a != NULL; a = a->outchain)
    newarc(nfa, type, a->co, from, to);
}

/*
 * delsub - delete a sub-NFA, updating subre pointers if necessary
 *
 * This uses a recursive traversal of the sub-NFA, marking already-seen
 * states using their tmp pointer.
 */
static void delsub(struct nfa *nfa,
                   struct state *lp, /* the sub-NFA goes from here... */
                   struct state *rp) /* ...to here, *not* inclusive */
{
  assert(lp != rp);

  rp->tmp = rp; /* mark end */

  deltraverse(nfa, lp, lp);
  assert(lp->nouts == 0 && rp->nins == 0);            /* did the job */
  assert(lp->no != FREESTATE && rp->no != FREESTATE); /* no more */

  rp->tmp = NULL; /* unmark end */
  lp->tmp = NULL; /* and begin, marked by deltraverse */
}

/*
 * deltraverse - the recursive heart of delsub
 * This routine's basic job is to destroy all out-arcs of the state.
 */
static void deltraverse(struct nfa *nfa, struct state *leftend,
                        struct state *s) {
  struct arc *a;
  struct state *to;

  if (s->nouts == 0) return;  /* nothing to do */
  if (s->tmp != NULL) return; /* already in progress */

  s->tmp = s; /* mark as in progress */

  while ((a = s->outs) != NULL) {
    to = a->to;
    deltraverse(nfa, leftend, to);
    assert(to->nouts == 0 || to->tmp != NULL);
    freearc(nfa, a);
    if (to->nins == 0 && to->tmp == NULL) {
      assert(to->nouts == 0);
      freestate(nfa, to);
    }
  }

  assert(s->no != FREESTATE);           /* we're still here */
  assert(s == leftend || s->nins != 0); /* and still reachable */
  assert(s->nouts == 0);                /* but have no outarcs */

  s->tmp = NULL; /* we're done here */
}

/*
 * dupnfa - duplicate sub-NFA
 *
 * Another recursive traversal, this time using tmp to point to duplicates
 * as well as mark already-seen states.  (You knew there was a reason why
 * it's a state pointer, didn't you? :-))
 */
static void dupnfa(struct nfa *nfa,
                   struct state *start, /* duplicate of subNFA starting here */
                   struct state *stop,  /* and stopping here */
                   struct state *from,  /* stringing duplicate from here */
                   struct state *to)    /* to here */
{
  if (start == stop) {
    newarc(nfa, EMPTY, 0, from, to);
    return;
  }

  stop->tmp = to;
  duptraverse(nfa, start, from);
  /* done, except for clearing out the tmp pointers */

  stop->tmp = NULL;
  cleartraverse(nfa, start);
}

/*
 * duptraverse - recursive heart of dupnfa
 */
static void duptraverse(struct nfa *nfa, struct state *s,
                        struct state *stmp) /* s's duplicate, or NULL */
{
  struct arc *a;

  if (s->tmp != NULL) return; /* already done */

  s->tmp = (stmp == NULL) ? newstate(nfa) : stmp;
  if (s->tmp == NULL) {
    assert(NISERR());
    return;
  }

  for (a = s->outs; a != NULL && !NISERR(); a = a->outchain) {
    duptraverse(nfa, a->to, (struct state *)NULL);
    if (NISERR()) break;
    assert(a->to->tmp != NULL);
    cparc(nfa, a, s->tmp, a->to->tmp);
  }
}

/*
 * cleartraverse - recursive cleanup for algorithms that leave tmp ptrs set
 */
static void cleartraverse(struct nfa *nfa, struct state *s) {
  struct arc *a;

  if (s->tmp == NULL) return;
  s->tmp = NULL;

  for (a = s->outs; a != NULL; a = a->outchain) cleartraverse(nfa, a->to);
}

/*
 * specialcolors - fill in special colors for an NFA
 */
static void specialcolors(struct nfa *nfa) {
  /* false colors for BOS, BOL, EOS, EOL */
  if (nfa->parent == NULL) {
    nfa->bos[0] = pseudocolor(nfa->cm);
    nfa->bos[1] = pseudocolor(nfa->cm);
    nfa->eos[0] = pseudocolor(nfa->cm);
    nfa->eos[1] = pseudocolor(nfa->cm);
  } else {
    assert(nfa->parent->bos[0] != COLORLESS);
    nfa->bos[0] = nfa->parent->bos[0];
    assert(nfa->parent->bos[1] != COLORLESS);
    nfa->bos[1] = nfa->parent->bos[1];
    assert(nfa->parent->eos[0] != COLORLESS);
    nfa->eos[0] = nfa->parent->eos[0];
    assert(nfa->parent->eos[1] != COLORLESS);
    nfa->eos[1] = nfa->parent->eos[1];
  }
}

/*
 * optimize - optimize an NFA
 */
static long                        /* re_info bits */
optimize(struct nfa *nfa, FILE *f) /* for debug output; NULL none */
{
#ifdef REG_DEBUG
  int verbose = (f != NULL) ? 1 : 0;

  if (verbose) fprintf(f, "\ninitial cleanup:\n");
#endif
  cleanup(nfa); /* may simplify situation */
#ifdef REG_DEBUG
  if (verbose) dumpnfa(nfa, f);
  if (verbose) fprintf(f, "\nempties:\n");
#endif
  fixempties(nfa, f); /* get rid of EMPTY arcs */
#ifdef REG_DEBUG
  if (verbose) fprintf(f, "\nconstraints:\n");
#endif
  pullback(nfa, f); /* pull back constraints backward */
  pushfwd(nfa, f);  /* push fwd constraints forward */
#ifdef REG_DEBUG
  if (verbose) fprintf(f, "\nfinal cleanup:\n");
#endif
  cleanup(nfa);        /* final tidying */
  return analyze(nfa); /* and analysis */
}

/*
 * pullback - pull back constraints backward to (with luck) eliminate them
 */
static void pullback(struct nfa *nfa, FILE *f) /* for debug output; NULL none */
{
  struct state *s;
  struct state *nexts;
  struct arc *a;
  struct arc *nexta;
  int progress;

  /* find and pull until there are no more */
  do {
    progress = 0;
    for (s = nfa->states; s != NULL && !NISERR(); s = nexts) {
      nexts = s->next;
      for (a = s->outs; a != NULL && !NISERR(); a = nexta) {
        nexta = a->outchain;
        if (a->type == '^' || a->type == BEHIND)
          if (pull(nfa, a)) progress = 1;
        assert(nexta == NULL || s->no != FREESTATE);
      }
    }
    if (progress && f != NULL) dumpnfa(nfa, f);
  } while (progress && !NISERR());
  if (NISERR()) return;

  for (a = nfa->pre->outs; a != NULL; a = nexta) {
    nexta = a->outchain;
    if (a->type == '^') {
      assert(a->co == 0 || a->co == 1);
      newarc(nfa, PLAIN, nfa->bos[a->co], a->from, a->to);
      freearc(nfa, a);
    }
  }
}

/*
 * pull - pull a back constraint backward past its source state
 * A significant property of this function is that it deletes at most
 * one state -- the constraint's from state -- and only if the constraint
 * was that state's last outarc.
 */
static int /* 0 couldn't, 1 could */
pull(struct nfa *nfa, struct arc *con) {
  struct state *from = con->from;
  struct state *to = con->to;
  struct arc *a;
  struct arc *nexta;
  struct state *s;

  if (from == to) { /* circular constraint is pointless */
    freearc(nfa, con);
    return 1;
  }
  if (from->flag) /* can't pull back beyond start */
    return 0;
  if (from->nins == 0) { /* unreachable */
    freearc(nfa, con);
    return 1;
  }

  /*
   * DGP 2007-11-15: Cloning a state with a circular constraint on its list
   * of outs can lead to trouble [Tcl Bug 1810038], so get rid of them
   * first.
   */
  for (a = from->outs; a != NULL; a = nexta) {
    nexta = a->outchain;
    switch (a->type) {
      case '^':
      case '$':
      case BEHIND:
      case AHEAD:
        if (from == a->to) freearc(nfa, a);
        break;
    }
  }

  /* first, clone from state if necessary to avoid other outarcs */
  if (from->nouts > 1) {
    s = newstate(nfa);
    if (NISERR()) return 0;
    assert(to != from);       /* con is not an inarc */
    copyins(nfa, from, s, 1); /* duplicate inarcs */
    cparc(nfa, con, s, to);   /* move constraint arc */
    freearc(nfa, con);
    from = s;
    con = from->outs;
  }
  assert(from->nouts == 1);

  /* propagate the constraint into the from state's inarcs */
  for (a = from->ins; a != NULL; a = nexta) {
    nexta = a->inchain;
    switch (combine(con, a)) {
      case INCOMPATIBLE: /* destroy the arc */
        freearc(nfa, a);
        break;
      case SATISFIED: /* no action needed */
        break;
      case COMPATIBLE: /* swap the two arcs, more or less */
        s = newstate(nfa);
        if (NISERR()) return 0;
        cparc(nfa, a, s, to); /* anticipate move */
        cparc(nfa, con, a->from, s);
        if (NISERR()) return 0;
        freearc(nfa, a);
        break;
      default:
        assert(NOTREACHED);
        break;
    }
  }

  /* remaining inarcs, if any, incorporate the constraint */
  moveins(nfa, from, to);
  dropstate(nfa, from); /* will free the constraint */
  return 1;
}

/*
 * pushfwd - push forward constraints forward to (with luck) eliminate them
 */
static void pushfwd(struct nfa *nfa, FILE *f) /* for debug output; NULL none */
{
  struct state *s;
  struct state *nexts;
  struct arc *a;
  struct arc *nexta;
  int progress;

  /* find and push until there are no more */
  do {
    progress = 0;
    for (s = nfa->states; s != NULL && !NISERR(); s = nexts) {
      nexts = s->next;
      for (a = s->ins; a != NULL && !NISERR(); a = nexta) {
        nexta = a->inchain;
        if (a->type == '$' || a->type == AHEAD)
          if (push(nfa, a)) progress = 1;
        assert(nexta == NULL || s->no != FREESTATE);
      }
    }
    if (progress && f != NULL) dumpnfa(nfa, f);
  } while (progress && !NISERR());
  if (NISERR()) return;

  for (a = nfa->post->ins; a != NULL; a = nexta) {
    nexta = a->inchain;
    if (a->type == '$') {
      assert(a->co == 0 || a->co == 1);
      newarc(nfa, PLAIN, nfa->eos[a->co], a->from, a->to);
      freearc(nfa, a);
    }
  }
}

/*
 * push - push a forward constraint forward past its destination state
 * A significant property of this function is that it deletes at most
 * one state -- the constraint's to state -- and only if the constraint
 * was that state's last inarc.
 */
static int /* 0 couldn't, 1 could */
push(struct nfa *nfa, struct arc *con) {
  struct state *from = con->from;
  struct state *to = con->to;
  struct arc *a;
  struct arc *nexta;
  struct state *s;

  if (to == from) { /* circular constraint is pointless */
    freearc(nfa, con);
    return 1;
  }
  if (to->flag) /* can't push forward beyond end */
    return 0;
  if (to->nouts == 0) { /* dead end */
    freearc(nfa, con);
    return 1;
  }

  /*
   * DGP 2007-11-15: Here we duplicate the same protections as appear in
   * pull() above to avoid troubles with cloning a state with a circular
   * constraint on its list of ins.  It is not clear whether this is
   * necessary, or is protecting against a "can't happen". Any test case
   * that actually leads to a freearc() call here would be a welcome
   * addition to the test suite.
   */
  for (a = to->ins; a != NULL; a = nexta) {
    nexta = a->inchain;
    switch (a->type) {
      case '^':
      case '$':
      case BEHIND:
      case AHEAD:
        if (a->from == to) freearc(nfa, a);
        break;
    }
  }

  /* first, clone to state if necessary to avoid other inarcs */
  if (to->nins > 1) {
    s = newstate(nfa);
    if (NISERR()) return 0;
    copyouts(nfa, to, s, 1);  /* duplicate outarcs */
    cparc(nfa, con, from, s); /* move constraint */
    freearc(nfa, con);
    to = s;
    con = to->ins;
  }
  assert(to->nins == 1);

  /* propagate the constraint into the to state's outarcs */
  for (a = to->outs; a != NULL; a = nexta) {
    nexta = a->outchain;
    switch (combine(con, a)) {
      case INCOMPATIBLE: /* destroy the arc */
        freearc(nfa, a);
        break;
      case SATISFIED: /* no action needed */
        break;
      case COMPATIBLE: /* swap the two arcs, more or less */
        s = newstate(nfa);
        if (NISERR()) return 0;
        cparc(nfa, con, s, a->to); /* anticipate move */
        cparc(nfa, a, from, s);
        if (NISERR()) return 0;
        freearc(nfa, a);
        break;
      default:
        assert(NOTREACHED);
        break;
    }
  }

  /* remaining outarcs, if any, incorporate the constraint */
  moveouts(nfa, to, from);
  dropstate(nfa, to); /* will free the constraint */
  return 1;
}

/*
 * combine - constraint lands on an arc, what happens?
 *
 * #def INCOMPATIBLE	1	// destroys arc
 * #def SATISFIED		2	// constraint satisfied
 * #def COMPATIBLE		3	// compatible but not satisfied yet
 */
static int combine(struct arc *con, struct arc *a) {
#define CA(ct, at) (((ct) << CHAR_BIT) | (at))

  switch (CA(con->type, a->type)) {
    case CA('^', PLAIN): /* newlines are handled separately */
    case CA('$', PLAIN):
      return INCOMPATIBLE;
      break;
    case CA(AHEAD, PLAIN): /* color constraints meet colors */
    case CA(BEHIND, PLAIN):
      if (con->co == a->co) return SATISFIED;
      return INCOMPATIBLE;
      break;
    case CA('^', '^'): /* collision, similar constraints */
    case CA('$', '$'):
    case CA(AHEAD, AHEAD):
    case CA(BEHIND, BEHIND):
      if (con->co == a->co) /* true duplication */
        return SATISFIED;
      return INCOMPATIBLE;
      break;
    case CA('^', BEHIND): /* collision, dissimilar constraints */
    case CA(BEHIND, '^'):
    case CA('$', AHEAD):
    case CA(AHEAD, '$'):
      return INCOMPATIBLE;
      break;
    case CA('^', '$'): /* constraints passing each other */
    case CA('^', AHEAD):
    case CA(BEHIND, '$'):
    case CA(BEHIND, AHEAD):
    case CA('$', '^'):
    case CA('$', BEHIND):
    case CA(AHEAD, '^'):
    case CA(AHEAD, BEHIND):
    case CA('^', LACON):
    case CA(BEHIND, LACON):
    case CA('$', LACON):
    case CA(AHEAD, LACON):
      return COMPATIBLE;
      break;
  }
  assert(NOTREACHED);
  return INCOMPATIBLE; /* for benefit of blind compilers */
}

/*
 * fixempties - get rid of EMPTY arcs
 */
static void fixempties(struct nfa *nfa,
                       FILE *f) /* for debug output; NULL none */
{
  struct state *s;
  struct state *s2;
  struct state *nexts;
  struct arc *a;
  struct arc *nexta;

  /*
   * First, get rid of any states whose sole out-arc is an EMPTY, since
   * they're basically just aliases for their successor.  The parsing
   * algorithm creates enough of these that it's worth special-casing this.
   */
  for (s = nfa->states; s != NULL && !NISERR(); s = nexts) {
    nexts = s->next;
    if (s->flag || s->nouts != 1) continue;
    a = s->outs;
    assert(a != NULL && a->outchain == NULL);
    if (a->type != EMPTY) continue;
    if (s != a->to) moveins(nfa, s, a->to);
    dropstate(nfa, s);
  }

  /*
   * Similarly, get rid of any state with a single EMPTY in-arc, by folding
   * it into its predecessor.
   */
  for (s = nfa->states; s != NULL && !NISERR(); s = nexts) {
    nexts = s->next;
    /* while we're at it, ensure tmp fields are clear for next step */
    assert(s->tmp == NULL);
    if (s->flag || s->nins != 1) continue;
    a = s->ins;
    assert(a != NULL && a->inchain == NULL);
    if (a->type != EMPTY) continue;
    if (s != a->from) moveouts(nfa, s, a->from);
    dropstate(nfa, s);
  }

  /*
   * For each remaining NFA state, find all other states that are reachable
   * from it by a chain of one or more EMPTY arcs.  Then generate new arcs
   * that eliminate the need for each such chain.
   *
   * If we just do this straightforwardly, the algorithm gets slow in
   * complex graphs, because the same arcs get copied to all intermediate
   * states of an EMPTY chain, and then uselessly pushed repeatedly to the
   * chain's final state; we waste a lot of time in newarc's duplicate
   * checking.  To improve matters, we decree that any state with only EMPTY
   * out-arcs is "doomed" and will not be part of the final NFA. That can be
   * ensured by not adding any new out-arcs to such a state. Having ensured
   * that, we need not update the state's in-arcs list either; all arcs that
   * might have gotten pushed forward to it will just get pushed directly to
   * successor states.  This eliminates most of the useless duplicate arcs.
   */
  for (s = nfa->states; s != NULL && !NISERR(); s = s->next) {
    for (s2 = emptyreachable(s, s); s2 != s && !NISERR(); s2 = nexts) {
      /*
       * If s2 is doomed, we decide that (1) we will always push arcs
       * forward to it, not pull them back to s; and (2) we can optimize
       * away the push-forward, per comment above.  So do nothing.
       */
      if (s2->flag || hasnonemptyout(s2)) replaceempty(nfa, s, s2);

      /* Reset the tmp fields as we walk back */
      nexts = s2->tmp;
      s2->tmp = NULL;
    }
    s->tmp = NULL;
  }

  if (NISERR()) return;

  /*
   * Now remove all the EMPTY arcs, since we don't need them anymore.
   */
  for (s = nfa->states; s != NULL; s = s->next) {
    for (a = s->outs; a != NULL; a = nexta) {
      nexta = a->outchain;
      if (a->type == EMPTY) freearc(nfa, a);
    }
  }

  /*
   * And remove any states that have become useless.  (This cleanup is not
   * very thorough, and would be even less so if we tried to combine it with
   * the previous step; but cleanup() will take care of anything we miss.)
   */
  for (s = nfa->states; s != NULL; s = nexts) {
    nexts = s->next;
    if ((s->nins == 0 || s->nouts == 0) && !s->flag) dropstate(nfa, s);
  }

  if (f != NULL) dumpnfa(nfa, f);
}

/*
 * emptyreachable - recursively find all states reachable from s by EMPTY arcs
 *
 * The return value is the last such state found.  Its tmp field links back
 * to the next-to-last such state, and so on back to s, so that all these
 * states can be located without searching the whole NFA.
 *
 * The maximum recursion depth here is equal to the length of the longest
 * loop-free chain of EMPTY arcs, which is surely no more than the size of
 * the NFA, and in practice will be a lot less than that.
 */
static struct state *emptyreachable(struct state *s, struct state *lastfound) {
  struct arc *a;

  s->tmp = lastfound;
  lastfound = s;
  for (a = s->outs; a != NULL; a = a->outchain) {
    if (a->type == EMPTY && a->to->tmp == NULL)
      lastfound = emptyreachable(a->to, lastfound);
  }
  return lastfound;
}

/*
 * replaceempty - replace an EMPTY arc chain with some non-empty arcs
 *
 * The EMPTY arc(s) should be deleted later, but we can't do it here because
 * they may still be needed to identify other arc chains during fixempties().
 */
static void replaceempty(struct nfa *nfa, struct state *from,
                         struct state *to) {
  int fromouts;
  int toins;

  assert(from != to);

  /*
   * Create replacement arcs that bypass the need for the EMPTY chain.  We
   * can do this either by pushing arcs forward (linking directly from
   * "from"'s predecessors to "to") or by pulling them back (linking
   * directly from "from" to "to"'s successors).  In general, we choose
   * whichever way creates greater fan-out or fan-in, so as to improve the
   * odds of reducing the other state to zero in-arcs or out-arcs and
   * thereby being able to delete it.  However, if "from" is doomed (has no
   * non-EMPTY out-arcs), we must keep it so, so always push forward in that
   * case.
   *
   * The fan-out/fan-in comparison should count only non-EMPTY arcs.  If
   * "from" is doomed, we can skip counting "to"'s arcs, since we want to
   * force taking the copyins path in that case.
   */
  fromouts = nonemptyouts(from);
  toins = (fromouts == 0) ? 1 : nonemptyins(to);

  if (fromouts > toins) {
    copyouts(nfa, to, from, 0);
    return;
  }

  if (fromouts < toins) {
    copyins(nfa, from, to, 0);
    return;
  }

  /*
   * fromouts == toins.  Decide on secondary issue: copy fewest arcs.
   *
   * Doesn't seem to be worth the trouble to exclude empties from these
   * comparisons; that takes extra time and doesn't seem to improve the
   * resulting graph much.
   */
  if (from->nins > to->nouts) {
    copyouts(nfa, to, from, 0);
    return;
  } else {
    copyins(nfa, from, to, 0);
    return;
  }
}

/*
 * cleanup - clean up NFA after optimizations
 */
static void cleanup(struct nfa *nfa) {
  struct state *s;
  struct state *nexts;
  int n;

  /* clear out unreachable or dead-end states */
  /* use pre to mark reachable, then post to mark can-reach-post */
  markreachable(nfa, nfa->pre, (struct state *)NULL, nfa->pre);
  markcanreach(nfa, nfa->post, nfa->pre, nfa->post);
  for (s = nfa->states; s != NULL; s = nexts) {
    nexts = s->next;
    if (s->tmp != nfa->post && !s->flag) dropstate(nfa, s);
  }
  assert(nfa->post->nins == 0 || nfa->post->tmp == nfa->post);
  cleartraverse(nfa, nfa->pre);
  assert(nfa->post->nins == 0 || nfa->post->tmp == NULL);
  /* the nins==0 (final unreachable) case will be caught later */

  /* renumber surviving states */
  n = 0;
  for (s = nfa->states; s != NULL; s = s->next) s->no = n++;
  nfa->nstates = n;
}

/*
 * markreachable - recursive marking of reachable states
 */
static void markreachable(
    struct nfa *nfa, struct state *s,
    struct state *okay, /* consider only states with this mark */
    struct state *mark) /* the value to mark with */
{
  struct arc *a;

  if (s->tmp != okay) return;
  s->tmp = mark;

  for (a = s->outs; a != NULL; a = a->outchain)
    markreachable(nfa, a->to, okay, mark);
}

/*
 * markcanreach - recursive marking of states which can reach here
 */
static void markcanreach(
    struct nfa *nfa, struct state *s,
    struct state *okay, /* consider only states with this mark */
    struct state *mark) /* the value to mark with */
{
  struct arc *a;

  if (s->tmp != okay) return;
  s->tmp = mark;

  for (a = s->ins; a != NULL; a = a->inchain)
    markcanreach(nfa, a->from, okay, mark);
}

/*
 * analyze - ascertain potentially-useful facts about an optimized NFA
 */
static long /* re_info bits to be ORed in */
analyze(struct nfa *nfa) {
  struct arc *a;
  struct arc *aa;

  if (nfa->pre->outs == NULL) return REG_UIMPOSSIBLE;
  for (a = nfa->pre->outs; a != NULL; a = a->outchain)
    for (aa = a->to->outs; aa != NULL; aa = aa->outchain)
      if (aa->to == nfa->post) return REG_UEMPTYMATCH;
  return 0;
}

/*
 * compact - compact an NFA
 */
static void compact(struct nfa *nfa, struct cnfa *cnfa) {
  struct state *s;
  struct arc *a;
  size_t nstates;
  size_t narcs;
  struct carc *ca;
  struct carc *first;

  assert(!NISERR());

  nstates = 0;
  narcs = 0;
  for (s = nfa->states; s != NULL; s = s->next) {
    nstates++;
    narcs += 1 + s->nouts + 1;
    /* 1 as a fake for flags, nouts for arcs, 1 as endmarker */
  }

  cnfa->states = (struct carc **)MALLOC(nstates * sizeof(struct carc *));
  cnfa->arcs = (struct carc *)MALLOC(narcs * sizeof(struct carc));
  if (cnfa->states == NULL || cnfa->arcs == NULL) {
    if (cnfa->states != NULL) FREE(cnfa->states);
    if (cnfa->arcs != NULL) FREE(cnfa->arcs);
    NERR(REG_ESPACE);
    return;
  }
  cnfa->nstates = nstates;
  cnfa->pre = nfa->pre->no;
  cnfa->post = nfa->post->no;
  cnfa->bos[0] = nfa->bos[0];
  cnfa->bos[1] = nfa->bos[1];
  cnfa->eos[0] = nfa->eos[0];
  cnfa->eos[1] = nfa->eos[1];
  cnfa->ncolors = maxcolor(nfa->cm) + 1;
  cnfa->flags = 0;

  ca = cnfa->arcs;
  for (s = nfa->states; s != NULL; s = s->next) {
    assert((size_t)s->no < nstates);
    cnfa->states[s->no] = ca;
    ca->co = 0; /* clear and skip flags "arc" */
    ca++;
    first = ca;
    for (a = s->outs; a != NULL; a = a->outchain) switch (a->type) {
        case PLAIN:
          ca->co = a->co;
          ca->to = a->to->no;
          ca++;
          break;
        case LACON:
          assert(s->no != cnfa->pre);
          ca->co = (color)(cnfa->ncolors + a->co);
          ca->to = a->to->no;
          ca++;
          cnfa->flags |= HASLACONS;
          break;
        default:
          assert(NOTREACHED);
          break;
      }
    carcsort(first, ca - 1);
    ca->co = COLORLESS;
    ca->to = 0;
    ca++;
  }
  assert(ca == &cnfa->arcs[narcs]);
  assert(cnfa->nstates != 0);

  /* mark no-progress states */
  for (a = nfa->pre->outs; a != NULL; a = a->outchain)
    cnfa->states[a->to->no]->co = 1;
  cnfa->states[nfa->pre->no]->co = 1;
}

/*
 * carcsort - sort compacted-NFA arcs by color
 *
 * Really dumb algorithm, but if the list is long enough for that to matter,
 * you're in real trouble anyway.
 */
static void carcsort(struct carc *first, struct carc *last) {
  struct carc *p;
  struct carc *q;
  struct carc tmp;

  if (last - first <= 1) return;

  for (p = first; p <= last; p++)
    for (q = p; q <= last; q++)
      if (p->co > q->co || (p->co == q->co && p->to > q->to)) {
        assert(p != q);
        tmp = *p;
        *p = *q;
        *q = tmp;
      }
}

/*
 * freecnfa - free a compacted NFA
 */
static void freecnfa(struct cnfa *cnfa) {
  assert(cnfa->nstates != 0); /* not empty already */
  cnfa->nstates = 0;
  FREE(cnfa->states);
  FREE(cnfa->arcs);
}

/*
 * dumpnfa - dump an NFA in human-readable form
 */
static void dumpnfa(struct nfa *nfa, FILE *f) {
#ifdef REG_DEBUG
  struct state *s;

  fprintf(f, "pre %d, post %d", nfa->pre->no, nfa->post->no);
  if (nfa->bos[0] != COLORLESS) fprintf(f, ", bos [%ld]", (long)nfa->bos[0]);
  if (nfa->bos[1] != COLORLESS) fprintf(f, ", bol [%ld]", (long)nfa->bos[1]);
  if (nfa->eos[0] != COLORLESS) fprintf(f, ", eos [%ld]", (long)nfa->eos[0]);
  if (nfa->eos[1] != COLORLESS) fprintf(f, ", eol [%ld]", (long)nfa->eos[1]);
  fprintf(f, "\n");
  for (s = nfa->states; s != NULL; s = s->next) dumpstate(s, f);
  if (nfa->parent == NULL) dumpcolors(nfa->cm, f);
  fflush(f);
#endif
}

#ifdef REG_DEBUG /* subordinates of dumpnfa */

/*
 * dumpstate - dump an NFA state in human-readable form
 */
static void dumpstate(struct state *s, FILE *f) {
  struct arc *a;

  fprintf(f, "%d%s%c", s->no, (s->tmp != NULL) ? "T" : "",
          (s->flag) ? s->flag : '.');
  if (s->prev != NULL && s->prev->next != s) fprintf(f, "\tstate chain bad\n");
  if (s->nouts == 0)
    fprintf(f, "\tno out arcs\n");
  else
    dumparcs(s, f);
  fflush(f);
  for (a = s->ins; a != NULL; a = a->inchain) {
    if (a->to != s)
      fprintf(f, "\tlink from %d to %d on %d's in-chain\n", a->from->no,
              a->to->no, s->no);
  }
}

/*
 * dumparcs - dump out-arcs in human-readable form
 */
static void dumparcs(struct state *s, FILE *f) {
  int pos;

  assert(s->nouts > 0);
  /* printing arcs in reverse order is usually clearer */
  pos = dumprarcs(s->outs, s, f, 1);
  if (pos != 1) fprintf(f, "\n");
}

/*
 * dumprarcs - dump remaining outarcs, recursively, in reverse order
 */
static int /* resulting print position */
dumprarcs(struct arc *a, struct state *s, FILE *f,
          int pos) /* initial print position */
{
  if (a->outchain != NULL) pos = dumprarcs(a->outchain, s, f, pos);
  dumparc(a, s, f);
  if (pos == 5) {
    fprintf(f, "\n");
    pos = 1;
  } else
    pos++;
  return pos;
}

/*
 * dumparc - dump one outarc in readable form, including prefixing tab
 */
static void dumparc(struct arc *a, struct state *s, FILE *f) {
  struct arc *aa;
  struct arcbatch *ab;

  fprintf(f, "\t");
  switch (a->type) {
    case PLAIN:
      fprintf(f, "[%ld]", (long)a->co);
      break;
    case AHEAD:
      fprintf(f, ">%ld>", (long)a->co);
      break;
    case BEHIND:
      fprintf(f, "<%ld<", (long)a->co);
      break;
    case LACON:
      fprintf(f, ":%ld:", (long)a->co);
      break;
    case '^':
    case '$':
      fprintf(f, "%c%d", a->type, (int)a->co);
      break;
    case EMPTY:
      break;
    default:
      fprintf(f, "0x%x/0%lo", a->type, (long)a->co);
      break;
  }
  if (a->from != s) fprintf(f, "?%d?", a->from->no);
  for (ab = &a->from->oas; ab != NULL; ab = ab->next) {
    for (aa = &ab->a[0]; aa < &ab->a[ABSIZE]; aa++)
      if (aa == a) break;    /* NOTE BREAK OUT */
    if (aa < &ab->a[ABSIZE]) /* propagate break */
      break;                 /* NOTE BREAK OUT */
  }
  if (ab == NULL) fprintf(f, "?!?"); /* not in allocated space */
  fprintf(f, "->");
  if (a->to == NULL) {
    fprintf(f, "NULL");
    return;
  }
  fprintf(f, "%d", a->to->no);
  for (aa = a->to->ins; aa != NULL; aa = aa->inchain)
    if (aa == a) break;              /* NOTE BREAK OUT */
  if (aa == NULL) fprintf(f, "?!?"); /* missing from in-chain */
}
#endif /* REG_DEBUG */

/*
 * dumpcnfa - dump a compacted NFA in human-readable form
 */
#ifdef REG_DEBUG
static void dumpcnfa(struct cnfa *cnfa, FILE *f) {
  int st;

  fprintf(f, "pre %d, post %d", cnfa->pre, cnfa->post);
  if (cnfa->bos[0] != COLORLESS) fprintf(f, ", bos [%ld]", (long)cnfa->bos[0]);
  if (cnfa->bos[1] != COLORLESS) fprintf(f, ", bol [%ld]", (long)cnfa->bos[1]);
  if (cnfa->eos[0] != COLORLESS) fprintf(f, ", eos [%ld]", (long)cnfa->eos[0]);
  if (cnfa->eos[1] != COLORLESS) fprintf(f, ", eol [%ld]", (long)cnfa->eos[1]);
  if (cnfa->flags & HASLACONS) fprintf(f, ", haslacons");
  fprintf(f, "\n");
  for (st = 0; st < cnfa->nstates; st++)
    dumpcstate(st, cnfa->states[st], cnfa, f);
  fflush(f);
}
#endif

#ifdef REG_DEBUG /* subordinates of dumpcnfa */

/*
 * dumpcstate - dump a compacted-NFA state in human-readable form
 */
static void dumpcstate(int st, struct carc *ca, struct cnfa *cnfa, FILE *f) {
  int i;
  int pos;

  fprintf(f, "%d%s", st, (ca[0].co) ? ":" : ".");
  pos = 1;
  for (i = 1; ca[i].co != COLORLESS; i++) {
    if (ca[i].co < cnfa->ncolors)
      fprintf(f, "\t[%ld]->%d", (long)ca[i].co, ca[i].to);
    else
      fprintf(f, "\t:%ld:->%d", (long)ca[i].co - cnfa->ncolors, ca[i].to);
    if (pos == 5) {
      fprintf(f, "\n");
      pos = 1;
    } else
      pos++;
  }
  if (i == 1 || pos != 1) fprintf(f, "\n");
  fflush(f);
}

#endif /* REG_DEBUG */
